A Match Bonus
What is the probability of tripling the bank before going bust when starting with 100 units?
Video poker game:
House edge=2.184%
Betting 1 unit a hand.
- 3-play: sd/round=16.64; sd/hand=9.61;
- 5-play: sd/round=23.28; sd/hand=10.41;
- 10-play: sd/round=38.56; sd/hand=12.19.
I am trying to take advantage of a match bonus. The bonus works like this: 50 units free money + 50 units real money. One is allowed to cash out only after reaching at least 300 units.
VPRookie
Thanks for your attention.
I’m going to play Deuces Wild, but this game is completely different from the classic one. This is why I pointed out the standard deviation only.
The good thing is the game you refer to (9-6-5 Double Bonus) has, I think, less variance than my game. BTW, how did you get the number 18.12%? Some software simulations?
Thanks for your readiness to help.
Here is the pay table:
Royal Flush 800
Four Deuces 400
Wild Royal Flush 100
5 of a Kind 50
Straight Flush 40
4 of a Kind 10
Full House 8
Flush 5
Straight 3
3 of a Kind 1
Looks great? But here are the drawbacks: One must pay not only for the deal, but for the draw too (matching the deal bet). Even when you have garbage you are obliged to draw and pay for it. Even if you hold all the 5 cards and press the start button you will pay for the draw you haven’t made. The only exception is when the player is dealt a winning hand. Then he can take his winnings without paying twice. According to my strategy such pat hands happen only 2.135% of the time. Thus, my number for the house edge (2.184%) could be called “element of risk”. The other thing that is out of the ordinary is discarded cards are returned back into the deck and have the same chance to be drawn along with the rest 47 cards.
One can play 3, 5 and 10 lines, but calculations for 1 line are welcome.
It would be nice if you are still in the mood for making some calculations for me.
VPRookie
Umm... Are you mixing up 1 coin pay table with 5 coins? or is this some wacky 5dimes pay table?Quote: VPRookieGaryJKoehler,
Thanks for your readiness to help.
Here is the pay table:
Royal Flush 800
Four Deuces 400
Wild Royal Flush 100
5 of a Kind 50
Straight Flush 40
4 of a Kind 10
Full House 8
Flush 5
Straight 3
3 of a Kind 1
Looks great? But here are the drawbacks: One must pay not only for the deal, but for the draw too (matching the deal bet). Even when you have garbage you are obliged to draw and pay for it. Even if you hold all the 5 cards and press the start button you will pay for the draw you haven’t made. The only exception is when the player is dealt a winning hand. Then he can take his winnings without paying twice. According to my strategy such pat hands happen only 2.135% of the time. Thus, my number for the house edge (2.184%) could be called “element of risk”. The other thing that is out of the ordinary is discarded cards are returned back into the deck and have the same chance to be drawn along with the rest 47 cards.
One can play 3, 5 and 10 lines, but calculations for 1 line are welcome.
It would be nice if you are still in the mood for making some calculations for me.
VPRookie
it's very strange.
Another item is necessary to understand for complete analysis is what happens when you have too few coins or units, as you call them, to play 3 lines. If I understand this thread, you are starting with 100 units (50 of yours plus 50 that are matched) and it costs 30, 50, or 100 to play 3, 5, or 10 lines at 10 units apiece for each hand. Thus, you may only have enough to play 1 hand of 10-play.
If you go below 30 units, do you forfeit the rest? Otherwise, what happens (since you do not have enough to make another complete bet)?
Quote: VPRookieGaryJKoehler,
Thanks for your readiness to help.
But here are the drawbacks: One must pay not only for the deal, but for the draw too (matching the deal bet). .... The other thing that is out of the ordinary is discarded cards are returned back into the deck and have the same chance to be drawn along with the rest 47 cards.
VPRookie
The deal-draw issue impacts EV. But, getting the outcome probabilities would be a bit challenging since none of my software allows for the recycling of cards. Without those, computing exact Gambler's Ruin probabilities would be impossible. So, until I add some code for recycling, I can't help much here.
Quote: RomesIt's strange because it's a double pay... I forget what the Wiz called them but he did a write up on them I think late last year. It's where you have to pay the coin in for the deal and again for the draw.
I think you are referring to the Super Hand games.
Quote: VPRookieGaryJKoehler,
Thanks for your readiness to help.
Here is the pay table:
Royal Flush 800
Four Deuces 400
Wild Royal Flush 100
5 of a Kind 50
Straight Flush 40
4 of a Kind 10
Full House 8
Flush 5
Straight 3
3 of a Kind 1
Looks great? But here are the drawbacks: One must pay not only for the deal, but for the draw too (matching the deal bet). Even when you have garbage you are obliged to draw and pay for it. Even if you hold all the 5 cards and press the start button you will pay for the draw you haven’t made. The only exception is when the player is dealt a winning hand. Then he can take his winnings without paying twice. According to my strategy such pat hands happen only 2.135% of the time. Thus, my number for the house edge (2.184%) could be called “element of risk”. The other thing that is out of the ordinary is discarded cards are returned back into the deck and have the same chance to be drawn along with the rest 47 cards.
One can play 3, 5 and 10 lines, but calculations for 1 line are welcome.
It would be nice if you are still in the mood for making some calculations for me.
VPRookie
Just curious, what is this game called? Are there other varieties, like Jacks or Better, Bonus Poker, etc.?
The recycling of discards, by one estimate (not exact calculation), could involve a factor of 0.9616, so without taking into consideration the times when one does not have to make the draw coin-in, that reduces the pay schedule to a more believable 97.36%. This gets closer to the OP's assertion of the edge. Sorry about the sidetrip while I tried to understand what was going on in this unusual game.Quote: drrockThat pay schedule is 101.25% if you are allowed to draw to each hand, even with a double bet.
Quote: drrockAnother item is necessary to understand for complete analysis is what happens when you have too few coins or units, as you call them, to play 3 lines. If I understand this thread, you are starting with 100 units (50 of yours plus 50 that are matched) and it costs 30, 50, or 100 to play 3, 5, or 10 lines at 10 units apiece for each hand. Thus, you may only have enough to play 1 hand of 10-play.
If you go below 30 units, do you forfeit the rest? Otherwise, what happens (since you do not have enough to make another complete bet)?
I tried to simplify things because of the unusual betting.
1 unit = $1.97865 (average bet per hand – $1 on deal and $0.97865 on draw)
Thus, 3-line play consumes 1 unit for each of the 3 hands or 3 units for 1 round, which is 3*$1.97865=$5.93595.
5-line play consumes 5*$1.97865=$9.89325 per round.
10-line play consumes 10*$1.97865=$19.7865 per round.
1 unit = $1.97865 is the max bet per hand. One can reduce his bet down to 10 times, but thus he’ll reduce variance too. One can play 1 line, but odds are too bad. One can continue playing until his balance drops under $0.20.
100 units starting money = $200 ($100+$100)
Quote: GaryJKoehlerAnother question: If one is dealt a pat hand, say a Three of a Kind, and decides to play it discarding as perfect play dictates. Does he collect just on the final outcome or on the pat dealt hand AND the final outcome? I suspect the former (i.e., just on the final outcome)?
Just on the final outcome.
Quote: GaryJKoehlerJust curious, what is this game called? Are there other varieties, like Jacks or Better, Bonus Poker, etc.?
The game is called Deuces Wild. Yes, there are other varieties, like Bonus Poker; Deuces & Joker; 2 Jokers Wild Turbo 4x4 (1 Joker x2 x3 x4; 2 Jokers x4 x9 x16); Joker Double (Joker x2); Deuces & Joker Wild x3 (Joker x1 x2 x3); 2 Jokers Wild 3x3 (1 Joker x1 x2 x3; 2 Jokers x1 x4 x9). I have partially analyzed Bonus Poker and Deuces & Joker. These games return less than Deuces Wild. And the rest “Joker” games are beyond my abilities.
Quote: VPRookie
- 3-play: sd/round=16.64; sd/hand=9.61;
- 5-play: sd/round=23.28; sd/hand=10.41;
- 10-play: sd/round=38.56; sd/hand=12.19.
My calculations for the standard deviation are incorrect. I may try to recalculate them.
RSF 2.30265E-05
2222 0.000143782
WRSF 0.001859124
5K 0.002750224
SF 0.006365456
4K 0.055386853
FH 0.025340808
FL 0.022378869
STR 0.054302698
3K 0.256075977
Nothing 0.575373182
The number of hands only playing the dealt cards: 58,916 (out of 2,598,960). So the average bet size is 1.977331.
All this is assuming I haven't screwed-up somewhere. I'll double check later.
Quote: VPRookieJust on the final outcome.
The game is called Deuces Wild. Yes, there are other varieties, like Bonus Poker; Deuces & Joker; 2 Jokers Wild Turbo 4x4 (1 Joker x2 x3 x4; 2 Jokers x4 x9 x16); Joker Double (Joker x2); Deuces & Joker Wild x3 (Joker x1 x2 x3); 2 Jokers Wild 3x3 (1 Joker x1 x2 x3; 2 Jokers x1 x4 x9). I have partially analyzed Bonus Poker and Deuces & Joker. These games return less than Deuces Wild. And the rest “Joker” games are beyond my abilities.
Is there a general name for these types of games?
Maybe now it's Button Bandits....
Thanks for analyzing the game.
Could you now compute the probability of reaching $600 target before dropping under $6 (the required minimum to play one round of 3-line play)? One is allowed to get a smaller match bonus ($50). Thus he can play with a bank of $100 trying to reach $300. Of course, when one is trying for a smaller target and playing more lines he should have bigger chances because of the increased variance.
Quote: GaryJKoehlerI redid my code to handle recycled discarded cards for the draw and the two-step decision on dealt/draw. I get an EV of 0.981853 and STDev of 4.567 (per coin bet). I haven't double checked but I think these are the outcome probabilities:
RSF 2.30265E-05
2222 0.000143782
WRSF 0.001859124
5K 0.002750224
SF 0.006365456
4K 0.055386853
FH 0.025340808
FL 0.022378869
STR 0.054302698
3K 0.256075977
Nothing 0.575373182
The number of hands only playing the dealt cards: 58,916 (out of 2,598,960). So the average bet size is 1.977331.
All this is assuming I haven't screwed-up somewhere. I'll double check later.
My understanding is that you are starting with a bankroll of $100. You have two potential targets – either $300 or $600 (call it T).
I am assuming the bet size is 2 units (instead of the average 1.977331).
Suppose you chose to wager $X per pull (you choose a coin size and number of lines of play). Then your target is T/X starting with a bankroll of $100/X.
Here are some values assuming a max bet per hand.
| Bank | Targets | ||||||
|---|---|---|---|---|---|---|---|
| Coin Size | Lines | Bet Per Hand | (in Hand Units) | 300 | Ruin | 600 | Ruin |
| $0.25 | 1 | $2.50 | 40 | 120 | 0.782469 | 240 | 0.905525 |
| $1.00 | 1 | $10.00 | 10 | 30 | 0.843116 | 60 | 0.904253 |
| $0.25 | 3 | $7.50 | 13.33333333 | 40 | 0.8166 | 80 | 0.902074 |
| $1.00 | 3 | $30.00 | 3.333333333 | 10 | 0.856983 | 20 | 0.936096 |
| $0.25 | 5 | $12.50 | 8 | 24 | 0.858033 | 48 | 0.90047 |
| $1.00 | 5 | $50.00 | 2 | 6 | 0.862422 | 12 | 0.935585 |
Note that for the rows with fractional Bank values, the ruin probabilities are understated a bit since I used the integer part of the value.
Again, all of this is assuming I haven't screwed-up somewhere.
Quote: TwoFeathersATLUsed to call them One Armed Bandits ;-)
Maybe now it's Button Bandits....
My local has machines that where the arm was there us a controller on a wire that looks like a wii controller. You can sit back on tour chair and relax and have the controller in hand. There are buttons on it so you can press a button on it and control the machine.
Quote: GaryJKoehlerOh, the multi-line games are treated as more expensive single line games in the table above. More work is needed to actually compute the ruin values taking into account the different combinations for possible wins in a hand.
Taking into account the different combinations for multi-line games gives:
| Bank | Targets | ||||||
|---|---|---|---|---|---|---|---|
| Coin Size | Lines | Bet Per Hand | (in Hand Units) | 300 | Ruin | 600 | Ruin |
| $0.25 | 1 | $2.50 | 40 | 120 | 0.782469 | 240 | 0.9055254763 |
| $1.00 | 1 | $10.00 | 10 | 30 | 0.843116 | 60 | 0.9042534075 |
| $0.25 | 3 | $7.50 | 13.33333333 | 40 | 0.8033806909 | 80 | 0.893342075 |
| $1.00 | 3 | $30.00 | 3.333333333 | 10 | 0.8580094302 | 20 | 0.9151796834 |
| $0.25 | 5 | $12.50 | 8 | 24 | 0.8363216813 | 48 | 0.8856986665 |
| $1.00 | 5 | $50.00 | 2 | 6 | 0.8004598409 | 12 | 0.8593998425 |
As above, for fractional Bank values, the ruin probabilities are overstated using rounded values (not understated like I had - you actually start with more money with the fractional amounts).
And once again, all of this is assuming I haven't screwed-up somewhere.
Thanks for your efforts.
It seems, unfortunately, ruin probabilities are too high. It is clear one can get an edge if probability of ruin is less than 0.8333.
Please note, when one is trying for $600 his starting bank is $200. One is always trying to triple the bank. The max bet per hand is $2 ($1 on deal + $1 on draw). Could you compute only the following case?
- coin size $1;
- 1 coin;
- bet per hand $2;
- 3 lines;
- bet per round $6;
- starting bank $100;
- target $300;
Quote: VPRookieGaryJKoehler,
Thanks for your efforts.
It seems, unfortunately, ruin probabilities are too high. It is clear one can get an edge if probability of ruin is less than 0.8333.
Please note, when one is trying for $600 his starting bank is $200. One is always trying to triple the bank. The max bet per hand is $2 ($1 on deal + $1 on draw). Could you compute only the following case?
- coin size $1;
- 1 coin;
- bet per hand $2;
- 3 lines;
- bet per round $6;
- starting bank $100;
- target $300;
Sure:
| Bank | Target | ||||
|---|---|---|---|---|---|
| Coin Size | Lines | Bet Per Hand | (in Hand Units) | 300 | Ruin |
| $1.00 | 1 | $2.00 | 50 | 150 | 0.787371365 |
| $1.00 | 3 | $6.00 | 16 | 50 | 0.8007132675 |
| $1.00 | 3 | $6.00 | 17 | 50 | 0.7869818629 |
| $1.00 | 5 | $10.00 | 10 | 30 | 0.8064170612 |
